• Support PF! Buy your school textbooks, materials and every day products Here!

Combinations of samples problem

  • #1
189
0

Homework Statement



Suppose that three computer boards in a production run of forty are defective. A sample of five is to be selected to be checked for defects.
a. How many different samples can be chosen?
b. How many samples will contain at least one defective board?
c. What is the probability that a randomly chosen sample of five contains at least one defective board?





The Attempt at a Solution



A) ##\binom{40}{5} = \frac{40!}{5!(35!)} = 658\;008##

B) ##\binom{5}{1}+\binom{5}{2}+\binom{5}{3} = 25##

C) ##P(E) = \frac{N(E)}{N(S)} = \frac{25}{658\;008}##
 

Answers and Replies

  • #2
189
0
B) ##\binom{3}{1}\binom{37}{4}+\binom{3}{2}\binom{37}{3}+\binom{3}{3} \binom{37}{2} = 222\,111##

C) ##P(E) = \frac{N(E)}{N(S)} = \frac{222\,111}{658\,008} \approx 33.76\%##
 
  • #3
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,538
1,150
Your second attempt looks good.

Another way to calculate (B) is to figure out how many ways to select 5 good boards and then subtract that number from your answer to (A).
 

Related Threads for: Combinations of samples problem

Replies
5
Views
3K
  • Last Post
Replies
1
Views
5K
  • Last Post
Replies
7
Views
614
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
5K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
7
Views
2K
Top